Geysers on Io

Physical Explanation of Processes

Source of Driving Energy

The satellite Io in the Jupiter system of moons, shows evidence
of a substantial internal energy source. Speculation on the source of
that energy has offered many theories. Each seems to have major flaws.
A logical energy source can be present. Each time Io passes the three other
Galilean satellites in their paths around Jupiter, tidal forces
stretch and pull Io. These effects are great enough to explain the
heat source in Io. They resemble tidal forces but are somewhat different.

In 1979, the Voyager 2 spacecraft passed near to the planet
Jupiter. While there, its cameras were briefly turned toward
various of the satellites (moons) that orbit Jupiter. The pictures
taken of the satellite called Io showed unmistakable evidence
of geyser or volcano activity occurring while the picture was
being taken. Unfortunately, there have been few opportunities
to again get close up views of Io to learn more about the unusual
activity there. Therefore, theoreticians have speculated as to the
mechanics of the satellite that could drive such dynamic geyser activity.

The fact that Io is extremely close to Jupiter has led some scientists
to speculate that that closeness somehow generates tides within Io
that create frictional heating within it, and that resultant heat
drives the geyser activity. There would appear to be an error
in this logic. This paper will attempt to present a logical source
for the forces that deform Io and thus create the internal frictional
heating that drives the geyser activity.

The flaw in the logic is that just being near a massive gravitational
object does NOT necessarily create tidal forces within Io. If it was true
that Io rotated on its axis with a different period than it revolves
around the planet Jupiter, then that argument would have great
validity. Calculations can show that such a tide in the body of Io
would have deformed the surface immensely. Every few hours, when Jupiter would
pass overhead, the ground surface of Io would be lifted up nearly half
a mile. About 11 hours later, when Jupiter would be on the horizon,
the surface would have dropped nearly a whole mile, to be about
half a mile below the average surface of the satellite. If that effect
actually occurred, it would be almost like being on a permanent roller
coaster! Certainly, that much flexing of the body of Io would
supply plenty of internal frictional heating to drive the geysers.

The severe dynamics of such a situation rapidly had to synchronize the
rotation and revolution long ago. Io must certainly have a permanently
distorted shape due to the tidal forces created by Jupiter. The shape would
resemble a prolate spheroid, with its long axis directed toward
the center of Jupiter. My calculations suggest that the long axis
should be approximately one mile greater than the dimension in either
perpendicular axis. I am not aware if anyone ever tried to measure
this prolateness of Io. But the shape would be relatively unchanging,
since that long axis would stay closely directed at the center of
Jupiter, and therefore not generating any dynamic differential tidal
forces within Io. The shape might be measurable from the Earth. When
Io is near conjunction or opposition, we should be viewing its
minimum shape, which should be very nearly circular. A few hours
later, when it is near greatest elongation, we should be looking
at its profile, where the width of its image should be around
1 mile greater than its height. That's a difference from being
circular of about 0.06%, which may be measurable from Earth or
from the Hubble space telescope.

There are secondary effects, generally called perturbations,
that CAN create dynamic changes in the forces, and therefore act to
change the actual shape of Io, which creates the internal frictional
heating needed to supply the geysers' energy source.

If Io's orbit had significant inclination to the equatorial
plane of Jupiter, then the lobes along the prolate axis would
alternately point above and then below the center-of-mass of
Jupiter. This would induce continual torques so that Io
would oscillate North and South (using Jupiter's reference frame)
each orbit. Such oscillations would allow the differential
dynamic forces necessary to produce tidal heating. As it turns out,
however, Io is in an orbit that has quite small orbital inclination,
about 0.04 degrees. The tidal heating that could result would
appear to be insignificant. Io's orbit is very close to
being equatorial.

If Io's orbit had significant eccentricity, then a different source
of tidal forces could be developed. When Io was nearest Jupiter, the
prolate axis dimension would be increased. By being closer to Jupiter, both
the force attracting the nearest part of Io and the force attracting the
farthest part of Io would be increased, but the attraction on the part
nearest Jupiter would have incrementally greater attraction. This would
induce force differentials that would tend to stretch Io along the prolate
axis. THAT would be a tidal effect! Io has a rather circular orbit, but
it DOES have some eccentricity, (0.004). Calculations suggest that this
eccentricity would cause Io to change its prolate axis length,
to stretch and recover, by about
40 feet once each orbit (42 hours). This is a very significant effect.
(The Earth's solid-body tides due to the Moon's gravitation,
are less than one foot.) The
continuous stretching and rebounding of its long axis by a 40-foot
differential every 42 hours would definitely create a lot of internal
frictional heating. This seems like a very likely source of such energy.

There would appear to be another possible source of dynamic differential
tidal energy generation. The next large satellite out, Europa,
has an orbital period of approximately twice that of Io. That means
that Io passes Europa (a conjunction, from Jupiter's point-of-view)
each time around. Let's consider this carefully.

Remember that Io must be significantly prolate, along an axis radial from
the center of Jupiter, by as much as a mile. As Io approaches Europa
from behind, the gravitational forces due to Europa, on Io, will tend
to pull it forward, obviously, but it will also act to rotate Io.
This is much more similar to normal tidal analysis, where the
differential forces present have component vectors along the surface
of the satellite. Before the moment of opposition, the forces
cause a torque that would slightly rotate (the outer portion of) Io
forward. After opposition,
a nearly precisely identical opposite torque acts to rotate it backward.
(The fact that these two situations are infinitesimally different,
a second-order effect,
seems quite likely to be the explanation of the near synchronicity
of the four large Galilean moons, but that's a different subject!)

There would be two effects of this interaction. First, the forces
that first turn Io and then turn it back, represent dynamic differential
forces acting on Io and its interior. Second, and probably more
important, is that, once Io's prolate axis is no longer directed
exactly at the center of Jupiter, the much larger effects due to
Jupiter's gravity mentioned
above (similar to the orbital inclination discussion) would
come into play. This would act to dynamically keep distorting the
shape of Io around the time of each opposition with Europa.
Io would tend to "twist-flex", as the two short-range
gravitational forces tend to try to rotate it in opposite directions.

The same argument can be applied to Ganymede, a much more massive
satellite, but which Io passes at a greater distance. Occasionally,
the effect of Europa and Ganymede add, as in spring tides on Earth.
At other times, their total effect is reduced, as in neap tides
on Earth.

Conclusion

There appear to be two major effects that act to generate the
internal frictional heating in Io. The slight eccentricity of Io's
orbit should result in a prolate pulsing each revolution. The
differential gravitational effects of Europa and Ganymede on the
prolate lobes of Io, would act, both directly and indirectly,
to distort the shape of Io just before and just after each
opposition with each of those two other satellites.

Since both of the mechanisms proposed above as being the driving
forces are gravitational in nature, it seems reasonable to also
include some comments about additional unexplained gravitational
phenomena in the Galilean satellite system of Jupiter.

Mutual Perturbations of the Four Great Moons of Jupiter

In 1996, I chose to try to calculate the very rare event of
an eclipse of one of these four Galilean moons by another of them.
It was necessary to predict each of their future positions extremely
precisely. I found that current Gravitational Theory just doesn't have
a good clue about how to do that. The equations that exist to predict
their paths are almost entirely based on empirical observations. There are
hundreds of terms, developed from Fourier analysis of the observed
motions of the moons, many of which have dependencies on the periods
of the other moons' orbits, but they also have constant factors that
come exclusively from empirical observation. Current Gravitational Theory
can explain a pitiful portion of all the dynamics going
on there.

Additional, precise study of the motions and mutual perturbations of the
Galilean satellites should greatly increase our understanding
of basic Gravitational Theory.

It seems particularly intriguing that the ratios of the orbital periods
for the four large Galilean satellites of Jupiter are nearly
exact multiples of each other. Is this merely an amazing coincidence?
That seems doubtful. It seems much more likely that
the perturbations of the satellites on one another have somehow acted
to develop this synchronicity. A brief reference to this
possibility is mentioned in the Io discussion above. Careful analysis
of the existing empirical data may enable new insights. In addition,
computer simulations of the differential dynamics of one satellite
passing another, would seem to be especially promising.

To specify this premise a little more, as the satellites orbit
Jupiter, it often happens that they pass each other, which can be
called oppositions. There are subtle, second-order modifications
to the orbits of each as a result. This effectively is an example
of "forced vibration", a standard Physics and Engineering
analysis concept. The force vectors that exist as an
opposition is approaching, might seem to be exactly mirror-opposites of
those that exist as they separate after opposition. They are not.
The satellites are slightly affected (moved and given slightly
different velocities) from the situation they would have had
if they had not had to approach one another. This makes the
opposition encounter slightly asymmetric. This results in a
second-order effect of the opposition episode. If computer simulations
were invoked to track these tiny variations
for the equivalent of millions of years, better understanding of the
nearly synchronized orbits may result.

The forced vibration approach to analysis actually results in
a requirement for a NEAR synchronicity, and essentially suggests that
a pure synchronous situation would be unstable.

This effect is vaguely similar to the Regression of the Nodes of our Moon,
or about the process that causes Precession of the Earth. As the Moon
approaches a Node, its path is curved slightly toward the Ecliptic.
After it passes the Node, that effect is reversed, leaving no residual
effect except for the fact that the location of the Node passage had
very slightly regressed along the orbit.

In the case of an opposition passage of Io and Europa, the initial
acceleration of Io and the deceleration of Europa are exactly reversed
after the opposition, allowing each to leave with the same velocity
it would have had if no opposition had occurred. However, the second-order
effect is that Io gained a few feet along its orbit,
while Europa lost a few feet. Exactly how this might
result in the near synchronization of the orbits of the four Galilean
satellites is not clear. The forced vibration approach seems to
offer some intriguing possibilities. A separate essay on that is
linked below.

Hopefully, another quirk of the Galilean satellite system will
also be explained as well. All four of the Galilean satellites
can NEVER be on the same side of Jupiter at the same time! This fact
has been long recognized. It's just that no present theory can
explain why it's true!

As an aside on this topic, even a much simpler system has many
behaviors that are not fully understood. Our own Earth-Moon system is
VERY complex. When President Kennedy first announced that the
United States was going to put a man on the Moon, scientists were
concerned, because they couldn't predict precisely enough exactly
where the Moon would be! A HUGE effort was put forth to accomplish
that goal. By 1969, when the moon landings actually occurred, the
calculations were not yet complete! (They still aren't!) (But they
were accurate to within a few inches, which was good enough) The
calculations which presently best describe the motion of the Moon involves
hundreds of thousands of terms. Theory is FAR behind in actually
understanding the sources of many of those terms.

It would be nice to think that there was some elegantly simple way
of presenting all this so that the empirically observed results
could be predicted from theory. There doesn't presently seem any
traditional way to accomplish this. The resolution may require some entirely
new insight, such as Newton realizing that he needed to invent
Calculus to solve the problems he faced three centuries ago.

A possible area to investigate more precisely and thoroughly, is the
behavior of the Trojan asteroids. Our present Gravitational theory
is pretty good at describing and understanding TWO-BODY gravitational
interactions, but THREE-BODY (or more) are presently generally beyond
our theoretical expertise. One of the few exceptions is the behavior
of those Trojan asteroids. They orbit the Sun in meta-stable orbits
which have effectively the same radius as Jupiter's orbit, but they
permanently remain 60 degrees ahead of or behind that planet as they
orbit the Sun. There are several large Trojan asteroids in each
of these two groups. Several questions come to mind. How do they move
within their little groups? Do the orbit each other? Do they sometimes
crash into each other? What is the path of the center of mass of each
of the two groups? Does that point orbit the Sun at EXACTLY the same
radius as Jupiter does? Does that point experience any oscillation or
resonance (or ringing) phenomena? I have some preliminary thoughts where
there should be small resonances that occur with periods of odd-fraction
integers (1/7, 1/9 etc) of Jupiter's period. Much more research
is necessary in these areas, and they might contribute toward a more
complete theory for Gravitation.

A Different Io Subject

When I was calculating the precise orbits of the four Galilean
satellites during 1996, I came up with results that there would be
several mutual eclipses during the Summer of 1997. A couple of these
involved Io eclipsing the Sun's light from getting to Europa.
As it happens, Io has a larger diameter than Europa, so the eclipse
would be a total eclipse.

An event like that early that Summer was when Jupiter was not very
near opposition, from our viewpoint on Earth. In other words,
the Earth was a little off to the side of the sunlight that was
getting to Jupiter and its satellites.

This seemed to me to offer a unique opportunity for gaining some
data. If we aimed a spectrograph at Europa at any normal time,
we should get a pretty normal spectrum of reflected sunlight.
(The eclipse I had predicted for 1997 would have a duration of about
17 seconds.) If we took a spectrogram of Europa 0.5 second
before totality began, we should be able to collect some useful
information. The sunlight that would have arrived at Europa at
that moment had to have earlier passed within about 60 miles of the surface
of Io on its path from the Sun to Europa. If there was sulphur
or ionized sulphur or ionized sulphur dioxide (or anything else)
in an atmosphere surrounding Io, the sunlight that would later arrive
at Europa would have had to pass through those atmospheric materials
near Io, and we should get evidence of absorption lines in the spectrum
taken of Europa at that moment.

NOTE: In the repeating series of these mutual Galilean
eclipses, another series of them occurred during the year 2003.
There were bound to again be some Io eclipses of Europa, early or late
in the string of such events, such that the Earth is off to the
side. This last is necessary such that the image of Europa would
be as separated as possible from the brilliant image of Jupiter,
so a spectrogram of Europa was not contaminated with light from
Jupiter. As in 1997, it seems like an ideal way of confirming
the specific atmospheric components of Io.

I haven't done any calculations for the Saturnian system, but
if Titan ever eclipses any of the other Saturnian satellites,
a similar spectrogram of that satellite might give evidence
of the chemical composition of the atmosphere around Titan.